Question

$\angle 1$ and $\angle 2$ are complementary angles. if $m\angle 1 = (5x - 28)^\circ$ and $m\angle 2 = (8x - 25)^\circ$, then find the measure of $\angle 1$.

Explanation:

Step1: Recall complementary angles sum

Complementary angles sum to \(90^\circ\), so \(m\angle1 + m\angle2 = 90^\circ\).
Substitute the given expressions: \((5x - 28) + (8x - 25) = 90\).

Step2: Simplify and solve for \(x\)

Combine like terms: \(5x + 8x - 28 - 25 = 90\) → \(13x - 53 = 90\).
Add 53 to both sides: \(13x = 90 + 53\) → \(13x = 143\).
Divide by 13: \(x = \frac{143}{13} = 11\).

Step3: Find \(m\angle1\)

Substitute \(x = 11\) into \(m\angle1 = 5x - 28\):
\(m\angle1 = 5(11) - 28 = 55 - 28 = 27\).

Answer:

The measure of \(\angle1\) is \(27^\circ\).